SAT SHEET (calculators allowed)
33. If !15 15 ! x, then x A) -30 B) -15 C) 0 D) 15 E) 30 =
=
34. A dozen roses cost cost $15.60 and the cost of one rose rose and one lily together cost $4.50. What is the cost of one lily? A) $1.30 B) $3.20 C) $5.80 D) $11.10 E) $20.10 88 , 97 9 7 , 98 9 8 , 10 101 , 10 103 , an and 78 , then the 35. If temperatures at 1 p.m. p.m. during a week in August were: 81 , 88 median temperature was A) 81 B) 88 C) 97 D) 98 E) 103 °
°
°
°
°
°
°
°
°
°
°
°
36. If points A and B above are two vertices vertices of an equilateral triangle, triangle, what is the perimeter of the triangle? A) 12 B) 15 C) 16 D) 22 E) 25 37. If the earth turns through 1 ?
360° longitude
in 24 hours, how many minutes does it take for the earth to revolve
°
A)
1 4
minute B) 4 minutes C) 6 minutes D) 15 minutes E) 30 minutes
38. If x is an even integer and y is an odd integer, then which of the following must be even? I. xy
II.
x( x + y )
III.
xy ! 2
2
A) I only B) I and II only C) II and III only D) I and III only E) I, II, and III 39. A set of math exams are numbered in order from 1 to 49. Ms. Jacobsen is going to correct some of the tests. She selects the third paper and every ninth paper thereafter. What is the number of the last paper she corrects? A) 45 B) 46 C) 47 D) 48 E) 49
SAT SHEET (calculators allowed)
Note: Figure not drawn to scale 40. What is the value of a + b? A) 120 B) 150 C) 180 D) 210 E) 240 41. If 5 3 = 25 , then x = A) 1 B) 2 C) 3 D) 4 E) 5 x +
x
42. In triangle ABC above, side a is 100% greater than side b and side c is 2 feet longer than side b. What is the length of side a if the perimeter equals 132 feet? A) 26 feet B) 32.5 feet C) 52 feet D) 65 feet E) 67 feet 43. In a group of 44 students, 26 are boys. If 33 of the students have a driver’s license and if 5 girls do not have a driver’s license, how many boys have a driver’s license? A) 10 B) 13 C) 15 D) 18 E) 20 44. If a number multiplied by 10 is the same as 10 less than the number, what is the number? A) !
10 9
B) !
12 11
C) !1 D) !
45. The average of three fractions is
2 5
10 11
E) !
1 12
B)
7 60
C)
2 15
D)
11 12
10
. If two of the fractions are
fraction? A)
9
E)
6 5
1 3
and
3 4
, what is the value of the missing
SAT SHEET (calculators allowed)
46. If nx = d + x, what is x in terms of n and d ? A)
d
+
n
n
B) d (n – 1) C)
d n !1
D) d (n + 1) E)
d n +1
47. If the isosceles triangle and the square have the same area, in terms of s, what is the altitude h of the triangle? A) s B) 2 s C) s 2 D) 2 s 2 E) s 3 48. If 1 ! j ! k ! 100, and j and k are integers, what is the greatest possible value of A) 0 B)
1 2
C)
97 98
D)
99 100
jk
?
E) 1
49. If circle R, in the figure above, is tangent to side AC and has a circumference of side AC ? A) 2 2 + 2 B) 4 2 C) 3 2 + 2 D) 4 + 2 2 E) 4 + 4 2 50. If xy = !6 and y 2 21 ! x 2 , what is the value of ( x ! y )2 ? A) 9 B) 15 C) 27 D) 33 E) 39 =
k! j
4!
, what is the length of
SAT SHEET (calculators allowed)
51. The price of a dress is m dollars and the price of a coat is p dollars. If the store gives a 25% discount on the dress and a 40% discount on the coat, then the dress and the coat would each cost the same. What is the ratio of
m
?
p
A)
1 5
B)
5 8
C)
4 5
D)
5 4
E)
8 5
52. In the cube shown above, if diagonal FG in a face of the cube is 7 2 , and AE equals 3, what is the length of a diagonal of square ABCD? A) 5 B) 5 2 C) 7 D) 7 2 E) Cannot be determined from the information given 53. At the farmer’s market, pears are sold for $1.20 for the first point and $1.00 for each additional pound. If the weight is rounded to the nearest whole pound, which of the following could express the cost of the pears as a function of n, where n is the number of pounds of pears purchased? A) f (n) 2.2n B) f (n ) = 1.2 + n C) f (n ) 1.2n D) f (n) = 2.2 + n E) f (n) = 0.2 + n =
=
54. Given: t varies inversely as p. If p is divided by 2, then t is A) decreased by 2 B) increased by 2 C) divided by 2 D) multiplied by 2 E) squared 55. If there is only one solution to this function, y = ax2 + bx + c, when y = 0, then the graph of the parabola could be
A)
B)
C)
D)
56. Which compound statement is equivalent to -4 ! x < 5 ? A) The union of {-4 ! x} and {x < 5} B) The intersection of {-4 ! x} and {x < 5} C) The union of {x ! 4} and {x < 5} D) the intersection of {x ! -4} and {x < 4} E) None of the statements above.
E)
SAT SHEET (calculators allowed)
x 0
f(x) -2
x 0
f(x) 7
1 2 3
0 0 4
1 2 3
7 7 7
57. If the tables above show values for he two functions f and g , then which of the following statements is true? 1
A) f (0) = g (0) B) f (1) = g (1) C) f (0) = g (0) – 5 D) f (2) = g (2) E) 2 f (3) = g (3) + 1 3
58. T-cells, under certain stimulus, show a growth rate of 25% every two hours. If we begin with 100 T-cells, to the nearest integer, how many T-cells are present after 12 hours? A) 250 B) 300 C) 381 D) 400 E) 1,455 59. Which of the following is a function whose domain is the set of real numbers and whose range is the set of all non-positive real numbers? A)
y
=
x
B)
y
=
x
2
C)
y
=
!
x
D)
y
=
! x
2
E)
y
=
x
2
60. In the figure above, a quarter circle is placed on a square target. If the radius of the quarter circle is the same as the length of a side of the square, what is the probability that a dart hits the square does not hit the quarter circle? A)
!
16
B)
2! 3
C)
4 " ! 4
D)
!
4
E)
!
2
Note: Figure not drawn to scale. 61. If AB = BC , what is the x-coordinate of point C ?
SAT SHEET (calculators allowed)
62. If
3 7
m=
7 3
n, then what is the value of
m
?
n
1
1
2
4
63. If Connie has 1 cups of flour and a cake recipe calls for 1 cups of flour, then what pecent of her flour will she use to make the cake? 64. For how many positive integers N is it true that 2 N + 10 < 23?
65. EFGH is a rectangular pool surrounded by a walkway. The uniform width of the walkway is 3. EF = 7 and FG = 5. What is the outer perimeter of the walkway?
66. On line segment AB above, points P and R are placed between points A and B so that AP = RB =
1
AB PR i
3
1 4
AB and
is what fraction of AB?
67. The base of an isosceles triangle is 30% less than one of the equal sides, and the perimeter is 81. How long is the shortest side?
68. In the figure above, the radius OA is 5 and the area of the shaded region is 15! . What is the degree measure of a?
SAT SHEET (calculators allowed)
69. A Halloween bag has sourballs and peppermint candies. The probability of selecting a peppermint candy is
3 11
. If there are exactly 32 sourballs in the bag, how many peppermint candies are in the bag?
70. If the slope of line l above is
1 3
, what is the area of the shaded portion?
71. If 75% of a group of 48 graduates are men and 1/3 of these men are law students, how many men in this group are law students? A) 4 B) 12 C) 16 D) 32 E) 36
72. Diagonals AC and BD in rectangle ABCD in the above figure intersect at point E . What is the sum of the perimeters of the shaded regions? A) 16 B) 20 C) 22 D) 26 E) 32 73.
If b = A)
1 5 1
625
, what is the value of B)
1 25
b 5
divided by
C) 1 D) 5 E) 25
5
b
?
SAT SHEET (calculators allowed)
74.
In the figure above, if the radius of the inscribed circle is ! , what is the area of the square? A) 2! 2 B) 4! C) 4! 2 D) 8! E) 16! 2
75.
Five out of 10 different positive integers are 10, 20, 30, 40, and 50. The other integers are greater than 70. If the average of the 10 integers is 100, what is the value of the largest possible integer? A) 99 B) 100 C) 150 D) 290 E) 560
76.
If
x
A) 77.
2
!9
a
=
a
B)
b
and
x ! 3
a +9 b
C)
=
b,
and
a !b
ab ! 0 ,
D)
then
a+b
79.
3=
E) ab
The areas of two circles differ by 36! square inches and their radii differ by 2 inches. Find the length of the radius, in inches, of the larger circle. A) 6 B) 8 C) 9 D) 10 E)12 Appetizer Saul
78.
x +
Entrée Beth
Dessert
First (5 Points) Second Beth (3 points) Third Max (1 Point) Saul, Beth, and Max were finalists in a cooking contest. The chart shows a partial display of points awarded. If there are no ties, what is the greatest number of points by which Saul’s total score could exceed Max’s total score? A) 8 B) 10 C) 12 D) 14 E) Cannot be determined from the information given If
a b c d ,
,
,
is defined for all positive integers as
A) -1 B) 0 C) 2 D) 7 E) 10
a
c
! b d , what is the value of 2,3,4,2 ?
SAT SHEET (calculators allowed)
80.
If the area of the rectangle is equal to the area of the semicircle and the length AD of the rectangle is 4, what is the width of the rectangle? A)
81.
!
4
B)
!
2
C)
!
D)
E)
2!
4!
Which statement is true about the data collected in the scatterplot above? A) There is a positive correlation and the slope of the line of best fit is close to 1. B) There is a positive correlation and the slope of the line of best fit is greater than 2. C) There is a positive correlation and the slope of the line of best fit is less than
1 2
D) There is a negative correlation and the slope of the line of best fit is close to -1. E) There is a negative correlation and the slope of the line of best fit is less than !
x
82.
If for all positive numbers x, A)
1 3
B) 1 C) 2 D) 3 E)
= 2
8 ! (!1) 3
1 2
x
, what is the value of
?
1 3
A = {-2, 1, 3} and B = {3,5,9} 83. Two number, x and y, are to be selected at random from sets A and B above. If x is selected from A and y is selected from B, what is the probability that x2 + y ! 9? A)
1 3
B)
4 9
C)
1 2
D)
5 9
E)
2 3
SAT SHEET (calculators allowed)
84. A liquid nitrogen container, shown above, has a radius of 5 and height of 12. If points P and Q lie on the circumference of the bottom and top of the cylinder, respectively, what is the greatest possible straight-line distance between P and Q? A) 12 B) 13 C) 14 D) 2 61 E) 22 85. A circular engine part must be made with a diameter of 8 inches and an error tolerance of at most 0.05 inch. Which of the following inequalities best describes the radius, r , of this engine part? A) r ! 4 " 0.025 B) r ! 4 " 0.10 C) r ! 0.05 " 4 D) r ! 0.025 E) r ! 4 " 0.05
x 1
f(x) 1
3 a+1
a b
86. Given the table above, and the function f ( x) = A) 5 B) 6 C) 7 D) 8.5 E) 9.5
2 x + 1 3
, what is the value of b?
SAT SHEET (calculators allowed)
ANSWERS
33. E 34. B 35. C 36. B 37. B 38. B 39. D 40. D 41. C 42. D 43. E 44. A 45. B 46. C 47. B 48. D 49. D 50. D 51. C 52. B 53. E 54. D 55. D 56. B 57. E 58. C 59. D
60. C 61. 8 62. 49/9 or 5.44 63. 83.3 64. 6 65. 48 66. 5/12 67. 21 68. 144 69. 12 70. 21/2 or 10.5 71. B 72. E 73. A 74. C 75. E 76. A 77. D 78. B 79. D 80. B 81. D 82. B 83. E 84. D 85. A 86. C
